Bonus for p416
Public  08/04/17  8xp  Math  87.5% 
Let $r_3(n) = \# \{ (x, y, z) \in \mathbb{Z}^3 \mid x^2 + y^2 + z^2 = n \}$.
For example, $r_3(0) = 1$, $r_3(1) = 6$ and $r_3(100) = 30$.
Let $S(n, m) = \sum \limits _{k=0}^{m1} r_3(n + k)$.
It can be verified that $S(1, 100) = 4168$ and $S(10^8, 100) = 6410310$.
Find $S(10^{17}, 100)$.
[My timing: 2.6 seconds (PyPy)]
Note: This would be hard without parigp and some papers.
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